Multiplicative distance

In algebraic geometry, $\backslash mu$ is said to be a multiplicative distance function over a field if it satisfies{{citation

| last = Hartshorne | first = Robin |author-link=Robin Hartshorne

| doi = 10.1007/978-0-387-22676-7

| isbn = 0-387-98650-2

| location = New York

| mr = 1761093

| page = 363

| publisher = Springer-Verlag

| series = Undergraduate Texts in Mathematics

| title = Geometry: Euclid and beyond

| url = https://books.google.com/books?id=EJCSL9S6la0C&pg=PA363

| year = 2000}}.

• $\backslash mu(AB)>1.\backslash ,$
• AB is congruent to A'B' iff $\backslash mu(AB)=\backslash mu(A\text{'}B\text{'}).\backslash ,$
• AB < A'B' iff
• $\backslash mu(AB+CD)=\backslash mu(AB)\backslash mu(CD).\backslash ,$